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Original Articles

Two-piece power normal distribution

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Pages 2619-2639 | Received 22 Jan 2019, Accepted 27 Sep 2019, Published online: 11 Oct 2019

References

  • Ardalan, A., S.M. Sadooghi-Alvandi, and A.R. Nematollahi. 2012. The two-piece normal-laplace distribution. Communications in Statistics - Theory and Methods 41 (20):3759–85. doi:10.1080/03610926.2011.564740.
  • Arnold, B.C., H.W. Gómez, and H.S. Salinas. 2009. On multiple constraint skewed models. Statistics 43 (3):279–93. doi:10.1080/02331880802357914.
  • Azzalini, A. 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics 12 (2):171–8.
  • Balakrishnan, N., and M.M. Ristić. 2016. Multivariate families of gamma-generated distributions with finite or infinite support above or below the diagonal. Journal of Multivariate Analysis 143:194–207. doi:10.1016/j.jmva.2015.09.012.
  • Birnbaum, Z.W., and S.C. Saunders. 1969. A new family of life distributions. Journal of Applied Probability 6 (2):319–27. doi:10.2307/3212003.
  • Bolfarine, H., G. Martínez-Flórez, and H.S. Salinas. 2018. Bimodal symmetric-asymmetric power-normal families. Communications in Statistics - Theory and Methods 47 (2):259–76. doi:10.1080/03610926.2013.765475.
  • Critchley, F., and M.C. Jones. 2008. Asymmetry and gradient asymmetry functions: Density-based skewness and kurtosis. Scandinavian Journal of Statistics 35 (3):415–37. doi:10.1111/j.1467-9469.2008.00599.x.
  • Gibbons, J.F., and S. Mylroie. 1973. Estimation of impurity profiles in ion‐implanted amorphous targets using joined half‐Gaussian distributions. Applied Physics Letters 22 (11):568–9. doi:10.1063/1.1654511.
  • Groeneveld, R.A., and G. Meeden. 1984. Measuring skewness and kurtosis. The Statistician 33 (4):391–9. doi:10.2307/2987742.
  • Hassan, M.Y., and R.H. Hijazi. 2010. A bimodal exponential power distribution. Pakistan Journal of Statistics 26 (2):379–96.
  • John, S. 1982. The three-parameter two-piece normal family of distributions and its fitting. Communications in Statistics - Theory and Methods 11 (8):879–85. doi:10.1080/03610928208828279.
  • Johnson, N.L. 1949. System of frequency curves generated by methods of translation. Biometrika 36 (1–2):149–76. doi:10.2307/2332539.
  • Johnson, N.L., S. Kotz, and N. Balakrishnan. 1970. Continuous univariate distributions. Vol. 1. Boston, MA: Houghton Mifflin.
  • Jones, M.C., and A. Pewsey. 2009. Sinh-arcsinh distributions. Biometrika 96 (4):761–80. doi:10.1093/biomet/asp053.
  • Kim, H.J. 2005. On a class of two-piece skew-normal distributions. Statistics 39 (6):537–53. doi:10.1080/02331880500366027.
  • Kimber, A.C. 1985. Methods for the two-piece normal distribution. Communications in Statistics - Theory and Methods 14 (1):235–45. doi:10.1080/03610928508828907.
  • Kimber, A.C., and C. Jeynes. 1987. An application of the truncated two-piece normal distribution to the measurement of depths of arsenic implants in silicon. Applied Statistics 36 (3):352–7. doi:10.2307/2347794.
  • Kumar, C.S., and M.R. Anusree. 2011. On a generalized mixture of standard normal and skew normal distributions. Statistics & Probability Letters 81 (12):1813–21. doi:10.1016/j.spl.2011.07.009.
  • Kumar, C.S., and M.R. Anusree. 2013. A generalized two-piece skew normal distribution and some of its properties. Statistics 47 (6):1370–80. doi:10.1080/02331888.2012.697269.
  • Kumar, C.S., and M.R. Anusree. 2014. On some properties of a general class of two-piece skew normal distribution. Journal of the Japan Statistical Society 44 (2):179–94. doi:10.14490/jjss.44.179.
  • Malachov, A.N. 1978. A cumulant analysis of random non-Gaussian processes and their transformations (in Russian). Soviet Radio. Moscow.
  • Mudholkar, G.S., and A.D. Hutson. 2000. The epsilon-skew-normal distribution for analyzing near-normal data. Journal of Statistical Planning and Inference 83 (2):291–309. doi:10.1016/S0378-3758(99)00096-8.
  • Moors, J.J.A. 1988. A quantile alternative for kurtosis. The Statistician 37 (1):25–32. doi:10.2307/2348376.
  • Pan, M.S., K.C. Chan, and C.W. Fok. 1995. The distribution of currency futures price changes: A two-piece mixture of normal approach. International Review of Economics & Finance 4 (1):69–78. doi:10.1016/1059-0560(95)90056-X.
  • Ristić, M. M., B. V. Popovic, K. Zografos, and N. Balakrishnan. 2018. Discrimination among bivariate beta-generated distributions. Statistics 52 (2):303–20. doi:10.1080/02331888.2017.1397156.
  • Rubio, F.J., and M.F. Steel. 2015. Bayesian modelling of skewness and kurtosis with two-piece scale and shape distributions. Electronic Journal of Statistics 9 (2):1884–912. doi:10.1214/15-EJS1060.
  • Van Zwet, W.R. 1964. Convex transformations of random variables. Amsterdam: Mathematics Centrum.
  • Zhu, D., and J.W. Galbraith. 2011. Modeling and forecasting expected shortfall with the generalized asymmetric student-t and asymmetric exponential power distributions. Journal of Empirical Finance 18 (4):765–78. doi:10.1016/j.jempfin.2011.05.006.

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